MATH-305   Geometry/Topology of Manifolds

An introduction to the study of manifolds, including both the geometric topology and the differential geometry of manifolds. The emphasis is on low-dimensional manifolds, especially curves and surfaces. Topics include the topology of subsets of Euclidean space, curves and surfaces in Euclidean space, the topological classification of compact connected surfaces, smooth curves and sur-faces, curvature, geodesics, the Gauss-Bonnet Theorem and the geometry of space. Prerequisites: Mathematics 270 or 271 and Mathematics 231, 256 or 355.